A young couple wants to have three children after they get m

A young couple wants to have three children after they get married. What is the probability that those three children will be all boys or all girls? please explain how you arrived at your answer and show your work.

Solution

Prob normally for a boy or a girl = 0.5 each

and each child is independent and there are two outcomes

Hence if X = No of girls born then X is Binomial (3, 0.5)

a) Prob all 3 are boys = P(X=0)

= 0.5³=0.125

b) Prob all 3 are girls = P(X=3)

= 0.5³

= 0.125